To find the volume of a triangular prism, you can use the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
where the base area is the area of the triangular base and the height is the length of the prism.
- Determine the base area of the triangle:
The base of the triangle is the width (4 feet), and the height of the triangle (the vertical height from the base to the top vertex) is given as 9 feet. The area of a triangle is calculated with the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case:
- Base = 4 feet
- Height = 9 feet
Calculating the area:
\[ \text{Area} = \frac{1}{2} \times 4 \times 9 = \frac{1}{2} \times 36 = 18 \text{ square feet} \]
- Calculate the volume of the prism:
Now that we have the area of the base, we can find the volume by multiplying the base area by the length (which is 16 feet):
\[ \text{Volume} = \text{Base Area} \times \text{Length} = 18 \text{ square feet} \times 16 \text{ feet} \]
Calculating the volume:
\[ \text{Volume} = 18 \times 16 = 288 \text{ cubic feet} \]
Thus, the volume of the triangular prism is 288 cubic feet.